Quadratic gravity

Quadratic gravity (QG) is an extension of general relativity obtained by adding all local quadratic-in-curvature terms to the Einstein–Hilbert Lagrangian.[1] Doing this makes the theory renormalizable.[1] This is one of numerous alternatives to general relativity.[2]: 63  It has been suggested that consistency with quantum chromodynamics requires these additional quadratic terms.[3]

The theory was originally proved to be renormalizable by Kellogg Stelle in 1977,[4] but had difficulty being accepted as a viable theory because of its introduction of a massive spin-2 ghost particle.[5][1] Aside from the massive ghost, the theory also predicts the existence of an additional scalar boson and the massless graviton[5], ensuring that general relativity is recovered at low energies. The additional scalar particle appears also in Alexei Starobinsky's work of 1980 on the early universe. In Starobinsky inflation, the scalar particle is responsible for cosmic inflation.[5][1]

QG, besides being renormalizable, has also been shown to feature a non-perturbative ultraviolet fixed point.[6] Unitarity, essential to a theory quantum gravity, has been established in appropriate constructions.[7][8][9] In scattering processes the unitarity of the S-matrix has been proved using the instability of the massive spin-2 particle.[10]

The relevant solutions are not unstable but metastable: when the energies are much below a threshold (that is high enough to describe the whole cosmology) runaways are avoided and the possible instability occurring when the bound is violated not only is compatible with cosmology but would also explain why we live in a homogeneous and isotropic universe.[9][11]

John Donoghue believes quadratic gravity could be a viable theory of quantum gravity.[5] He has reinterpreted its ghost particles as time-reversed unstable particles.[12][8]

Work has been directed towards using the Event Horizon Telescope to test for the possibility of QG being a valid theory.[13]

References

  1. ^ a b c d Salvio, Alberto (2018). "Quadratic Gravity". Frontiers in Physics. 6 (77) 77. arXiv:1804.09944. Bibcode:2018FrP.....6...77S. doi:10.3389/fphy.2018.00077.
  2. ^ Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio; Skordis, Constantinos (1 March 2012). "Modified gravity and cosmology". Physics Reports. Modified Gravity and Cosmology. 513 (1): 1–189. doi:10.1016/j.physrep.2012.01.001. ISSN 0370-1573.
  3. ^ Salvio, Alberto (2021). "Dimensional Transmutation in Gravity and Cosmology". Int. J. Mod. Phys. A. 36 (8n09, 2130006): 2130006–2130831. arXiv:2012.11608. Bibcode:2021IJMPA..3630006S. doi:10.1142/S0217751X21300064. S2CID 229349013.
  4. ^ Stelle, K. S. (15 August 1977). "Renormalization of higher-derivative quantum gravity". Physical Review D. 16 (4): 953–969. doi:10.1103/PhysRevD.16.953. ISSN 0556-2821.
  5. ^ a b c d Wood, Charlie (17 November 2025). "Old 'Ghost' Theory of Quantum Gravity Makes a Comeback". Quanta Magazine. Retrieved 18 November 2025.
  6. ^ Falls, Kevin; Ohta, Nobuyoshi; Percacci, Roberto (2020). "Towards the determination of the dimension of the critical surface in asymptotically safe gravity". Physics Letters B. 810 (135773) 135773. arXiv:2004.04126. Bibcode:2020PhLB..81035773F. doi:10.1016/j.physletb.2020.135773.
  7. ^ Salvio, Alberto (1 July 2019). "Quasi-Conformal Models and the Early Universe". Eur.Phys.J.C. 79 (9). doi:10.1140/epjc/s10052-019-7267-5.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  8. ^ a b Kubo, Jisuke; Kuntz, Jeffrey (21 December 2022). "Spontaneous conformal symmetry breaking and quantum quadratic gravity". Physical Review D. 106 (12). doi:10.1103/PhysRevD.106.126015. ISSN 2470-0010.
  9. ^ a b Salvio, Alberto (11 April 2024). "A non-perturbative and background-independent formulation of quadratic gravity". JCAP. 07 (092). doi:10.1088/1475-7516/2024/07/092.
  10. ^ Donoghue, John F.; Menezes, Gabriel (2019). "Unitarity, stability and loops of unstable ghosts". Physical Review D. 100 (105006). arXiv:1908.02416. doi:10.1103/PhysRevD.100.105006.
  11. ^ Salvio, Alberto (25 February 2019). "Metastability in Quadratic Gravity". Physical Review D. 99 (10). doi:10.1103/PhysRevD.99.103507.
  12. ^ Donoghue, John F.; Menezes, Gabriel (3 May 2022). "On quadratic gravity". Il Nuovo Cimento C. 45 (2): 1–11. doi:10.1393/ncc/i2022-22026-7.
  13. ^ Daas, Jesse; Kuijpers, Kolja; Saueressig, Frank; Wondrak, Michael F.; Falcke, Heino (May 2023). "Probing quadratic gravity with the Event Horizon Telescope". Astronomy & Astrophysics. 673: A53. arXiv:2204.08480. Bibcode:2023A&A...673A..53D. doi:10.1051/0004-6361/202244080. ISSN 0004-6361.


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